First, all formulas of trigonometric function in senior high school
1, and the angle formula: sin(A+B)=sinAcosB+cosAsinB, sin(A-B)=sinAcosB-cosAsinB, cos(A+B)=cosAcosB-sinAsinB, cos(A-B)=cosAcosB+sinAsinB.
2. Sum and difference formulas of products: Sina Cosb =1/2 * (sin (a+b)+sin (a-b)), Cosa Sinb =1/2 * (sin (a+b)-sin (a-b)) and COSA.
3. Angle multiplication formula: sin2a = 2sina. Cosa cos2 a = Cosa 2-Sina 2 = 1-2 Sina 2 = 2 Cosa 2- 1 Tanya =(2 tana)/( 1-tana 2)。
Half-angle formula: sin(A/2)=√[( 1-cosA)/2], cos(A/2)=√[( 1+cosA)/2], tan (a/2) = √ [(/kloc-0).
4. Sine theorem: In any triangle, the ratio of the length of each side to the sine value of the corresponding angle is equal, that is, a/sinA=b/sinB=c/sinC.
5. Cosine theorem: In any triangle, the square of any one side is equal to the sum of the squares of the other two sides minus twice the product of cosine between these two sides and angle 6, that is, A 2 = B 2+C 2-2bc * COSA.
7. Tangent theorem: In any triangle, the ratio of the opposite side to the adjacent side of any side is equal to the ratio of the opposite side to the oblique side, that is, tanB=tan(π-(A+C)).
8. Sum formula of two angles: sin(A+B)=sinAcosB+cosAsinB, cos(A+B)=cosAcosB-sinAsinB, TAN (a+b) = (Tana +TANB)/( 1- Tana TANB).
9. Two-angle difference formula: sin(A-B)=sinAcosB-cosAsinB, cos(A-B)=cosAcosB+sinAsinB, TAN (a-b) = (Tana -TANB)/( 1+ Tana TANB).
Second, the definition of trigonometric function
Trigonometric function is one of the basic functions in mathematics, which is widely used in trigonometry, geometry, physics and other fields. The definition of trigonometric function is based on the relationship between angle and edge, usually taking right triangle as the basic unit.
Application of trigonometric function in mathematics;
The application of 1 and trigonometric functions in solving triangles;
When solving triangles, we often use trigonometric functions to solve problems. For example, if the side length and corner are known, other unknown side lengths and corners can be calculated by trigonometric function. In addition, we can also use trigonometric functions to prove some theorems, such as cosine theorem and sine theorem.
2. Application of trigonometric function in function image:
Trigonometric function is one of the common functions in mathematics, and it is also widely used in function images. For example, the images of sine function and cosine function are periodic, and these images can be used to simulate periodic changes. In addition, trigonometric functions are also widely used in signal processing and image processing.
3. The application of trigonometric function in analytic geometry;
In analytic geometry, we often use trigonometric functions to study the relationship between points and geometric figures such as circles and lines. For example, we can use trigonometric function to calculate the distance and angle between two points, and we can also use trigonometric function to study the properties of circles and ellipses.